A021004 Pisot sequence P(4,10).

4, 10, 25, 62, 154, 383, 953, 2371, 5899, 14677, 36517, 90856, 226054, 562433, 1399360, 3481674, 8662570, 21552885, 53624600, 133420548, 331956651, 825923891, 2054937811, 5112782731, 12720845913, 31650067929, 78746870040, 195925947300, 487473048845

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

Formula

Conjecture: a(n) = 2a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-6) (checked up to n = 1000)

Conjectured G.f.: (4+2 x+x^2-2 x^3-x^4-2 x^5)/(1-2 x-x^2-x^3+ x^4+x^6) - Harvey P. Dale, Mar 12 2011

Mathematica

RecurrenceTable[{a[n] == Ceiling[a[n - 1]^2/a[n - 2] - 1/2], a[0] == 4, a[1] == 10}, a, {n, 0, 28}] (* Michael De Vlieger, Aug 08 2016 *)

Prog

(PARI) pisotP(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));
  a
}
pisotP(50, 4, 10) \\ Colin Barker, Aug 08 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A362179 A033539 A020748 * A020709 A020734 A225301

Adjacent sequences: A021001 A021002 A021003 * A021005 A021006 A021007

Keyword

nonn

Author

R. K. Guy

Status

approved